Publications related to Contraction mapping

Recursive evaluation and iterative contraction of N-body equivariant features

Michele Ceriotti, Sergey Pozdnyakov, Jigyasa Nigam

Mapping an atomistic configuration to a symmetrized N-point correlation of a field associated with the atomic positions (e.g., an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algo ...

2020

Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Volkan Cevher, Paul Thierry Yves Rolland, Fabian Ricardo Latorre Gomez, Shaul Nadav Hallak

We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of stochastic proxi ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2020

Deep Spline Networks With Control Of Lipschitz Regularity

Michaël Unser, Shayan Aziznejad

The motivation for this work is to improve the performance of deep neural networks through the optimization of the individual activation functions. Since the latter results in an infinite-dimensional optimization problem, we resolve the ambiguity by search ...

IEEE2019

Avoidance of Convex and Concave Obstacles with Convergence ensured through Contraction

Aude Billard, Lukas Huber

This paper presents a closed-form approach to obstacle avoidance for multiple moving convex and star-shaped concave obstacles. The method takes inspiration in harmonic-potential fields. It inherits the convergence properties of harmonic potentials. We prov ...

2019

Distributed Inference over Multitask Graphs under Smoothness

Ali H. Sayed, Stefan Vlaski, Roula Nassif

This paper formulates a multitask optimization problem where agents in the network have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness condition over the graph. The smoothness requirement softens the tra ...

IEEE2018

Optimal reinsurance with multiple tranches

Semyon Malamud

Motivated by common practices in the reinsurance industry and in insurance markets such as Lloyd's, we study the general problem of optimal insurance contracts design in the presence of multiple insurance providers. We show that the optimal risk allocation ...

Elsevier Science Sa2016

Decomposition Strategies for Nonconvex Problems, a Parametric Approach

Jean-Hubert Hours

This thesis deals with the development of numerical methods for solving nonconvex optimisation problems by means of decomposition and continuation techniques. We first introduce a novel decomposition algorithm based on alternating gradient projections and ...

EPFL2016

A General Family of Morphed Nonlinear Phase Oscillators with Arbitrary Limit Cycle Shape

Auke Ijspeert, Mostafa Ajallooeian, Jesse van den Kieboom

We present a general family of nonlinear phase oscillators which can exhibit arbitrary limit cycle shapes and infinitely large basins of attraction. This general family is the superset of familiar control methods like PD-control over a periodic reference, ...

Elsevier Science Bv2013

The Two-Well Problem For Piecewise-Affine Maps

Bernard Dacorogna

In the two-well problem we look for a map u which satisfies Dirichlet boundary conditions and whose gradient Du assumes values in SO (2) A boolean OR SO (2) B = S-A boolean OR S-B, for two given invertible matrices A, B (an element of SO (2) A is of the fo ...

2012

Demosaicking by Alternating Projections: Theory and Fast One-Step Implementation

Martin Vetterli, Yue Lu, Mina Karzand

Color image demosaicking is a key process in the digital imaging pipeline. In this paper, we study a well-known and influential demosaicking algorithm based on alternating projections (AP), proposed by Gunturk, Altunbasak and Mersereau in 2002. Since its p ...

Institute of Electrical and Electronics Engineers2010